Cauchy number of the first kind

A number defined by b_n = b_n(0), where b_n(x) is a Bernoulli polynomial of the second kind, also called Cauchy numbers of the first kind. The first few for n = 0, 1, 2, ... are 1, 1/2, -1/6, 1/4, -19/30, 9/4, ... (OEIS A006232 and A006233). They are given by b_n = integral_0^1 (x)_n d x, where (x)_n is a falling factorial, and have exponential generating function E(x) = x/(ln(1 + x)) = 1 + (1!)/2 x - (2!)/6 x^2 + (3!)/4 x^3 + ....

Bernoulli number | Bernoulli polynomial of the second kind